Stability and non-stability of generalized radical cubic functional equation in quasi-$\beta$-Banach spaces

Iz. EL-Fassi, J. M. Rassias

The object of this paper is to solve the generalized radical cubic functional equation, and discuss the stability problem in quasi-$\beta$-Banach spaces and then the stability by using subadditive and subquadratic functions in ($\beta, p$)-Banach spaces for the generalized radical cubic functional equation. Also certain non-stability results are investigated via specific counterexamples. Our results are generalization of the main results which are established by Z. Alizadeh and A. G. Ghazanfari in 2016. 

Tbilisi Mathematical Journal, Vol. 12(3) (2019), pp. 175-190